General information
Below are the lectures offered by our working group in the winter semester.
If you would like to write a Bachelor's or Master's thesis in Statistics, please contact Prof. Redenbach.
Lectures in winter term
Below are the lectures offered by our working group in the winter term 2021/2022.
Mathematical Statistics
Contents
- Asymptotic analysis of M-estimators, especially of Maximum-Likelihood-estimators
- Bayes and Minimax-estimators
- Likelihood-ratio-tests: asymptotic analysis and examples (t-test, chi²-goodness-of-fit-test)
- Glivenko-Cantelli-theorem, Kolmogorov-Smirnov-test
- Differentiable statistic functionals and examples of applications (derivation of asymptotic results, robustness)
- Resampling methods on the basis of Bootstrap.
Stochastic Methods
Contents
Grundlagen der Wahrscheinlichkeitstheorie:
- Grundbegriffe der Wahrscheinlichkeitstheorie (Wahrscheinlichkeitsraum, Zufallsvariable, Verteilung),
- Verteilung reellwertiger Zufallsvariablen (Binomial-, Poisson-, Exponential- und Normalverteilung u.a.),
- Erwartungswert, Varianz, Kovarianz,
- Verteilung von Zufallsvektoren, multivariate Normalverteilung als Beispiel,
- Bedingte Wahrscheinlichkeit, Unabhängigkeit,
- Gesetz der großen Zahlen,
- Zentraler Grenzwertsatz.
Grundlagen der Statistik:
- Parameterschätzer,
- Intervallschätzer,
- Tests.
Ausblicke auf folgende Bereiche:
- Monte-Carlo-Simulation,
- Lineare Regression,
- Große Datenmengen und maschinelles Lernen,
- Markovketten.
Statistical Learning for Anomaly Detection and Change-Point Analysis
Contents
- Basics of machine/statistical learning,
- Classifiers in the context of anomality detection:
- logistic regression,
- neural networks,
- classification and regression trees (CART),
- other methods, e.g. random forest, support vector machines (SVMs),
- Outlier detection:
- isolation forest,
- one-class SVM,
- other methods, e.g. local outlier factor (LOF),
- Change-point detection:
- cumulative sum (CUSUM), moving sum (MOSUM),
- binary segmentation,
- other methods, e.g. pruned exact olinear time (PELT) change-point detection method.
The methods are explained and evaluated using selected examples.
Courses for students of other departments
Here you can find more lectures for students of other departments:
- Mathematics/Biostatistics 1
- Introduction to Stochastic Modeling of Cognitive Processes
- Mathematics for Economists
- etc.
The Reading Course serves as preparation for the Master's thesis. The assignment of topics takes place individually. Please contact Prof. Redenbach if you would like to take a Reading Course in Statistics.